Mathematics for the Liberal Arts Exam File Spring 2009 Exam #1 In exercises #1 - 5, a logical fallacy is exhibited. For each one, identify one of our fallacies that is exhibited in that argument or advertisement. 1.) Former major league pitcher Ross Grimsley, nicknamed "Scuzz," would not wash or change any part of his uniform as long as the team was winning, believing that washing or changing anything would jinx the team. 2.) "Buy new and improved CRUST™ toothpaste, the toothpaste used by more people than any toothpaste in the country!" 3.) "Eighty year old people don't need to go into nursing homes. After all my mother is 85 and she power-walks two miles each day, drives her car (safely), climbs stairs, does crosswords, and reads the daily paper." (adapted from http://www.fallacyfiles.org) 4.) "I have never seen a bear in this area so there must not be any bears around here." 5.) "If we allow unregulated harvesting of our forests then what are we going to do about the increase in abuse of the food stamp program." 6.) Construct a truth table for the following proposition. (not p q) (not q) 7.) For each of the following, writing "Yes" if it is a proposition (statement) or "No" if it is not. a.) Grab that fish! b.) Arkansas is larger than Rhode Island. c.) Bob Uecker is the best catcher of all-time. d.) Bob is 25 years old and Dave's dog is plaid. e.) Mickey Mouse was president of the United States in 1998. 8.) Draw a Venn diagram to illustrate the following proposition. All fish eat pizza and no fish ride bicycles. 9.) The part of a major league infield that is inside the bases is a square that is 90 feet on each side. What is its area in square centimeters? 10.) The following Venn diagram gives information about players on the New York Mets' roster as of September 15, 2007. The circle labeled "O" denotes players who are 30 years old or older. The circle labeled "H" denotes players who are 6 feet tall or taller. The circle labeled "R" denotes players who throw right-handed. (data from www.mlb.com) a.) How many players are under 6 feet tall? b.) What can you say about the player denoted by the "x?" c.) How many players are under 30 years old and throw right-handed? d.) What can you say about the player denoted by the "y?" 11.) Billy Bob's combination motor oil/salad dressing is on sale for $3.50 per gallon. He is now beginning to sell it in Mexico. What would the price be in pesos per liter? SHOW ALL NECESSARY WORK!! 12.) Tom threw a baseball 44.7 meters per second. Dave threw a ball 92 miles per hour. Who threw the ball faster, Tom or Dave? Be sure to show all necessary work. 13.) Walter Young, at 6-foot-5, 322-pounds, is believed to be the heaviest major league baseball player ever. Convert his height to centimeters and his weight to kilograms. 14.) At 4:32 p.m. on September 15, 2007, www.weather.com listed the temperature in Arkadelphia as being 78 degrees Fahrenheit. What is that in Celsius? 15.) In your drawer you have 15 identical green socks, 24 identical blue socks and 18 identical plaid socks. Without looking, you start pulling socks out of the drawer. a.) How many socks must you pull out so that it is certain you have a matching pair of socks? b.) How many socks must you pull out so that it is certain you have a matching pair of green socks? c.) How many socks must you pull out so that it is certain you have a matching pair of either plaid or blue socks? 16.) In a particular scout troop, 70% of the scouts have a compass, 75% have matches, 85% have a knife and 85% have a watch. What is the least percentage of the scouts that must have all four items? 17.) You have a seven minute hour glass and a four minute hour glass. You are cooking something that must be cooked for an exact amount of time. [Note: It is impossible to tell when an hour glass is exactly half empty, or has just one minute left, etc.] a.) How would you use the two hour glasses to time your cooking if you must cook for exactly three minutes? b.) How would you use the two hour glasses to time your cooking if you must cook for exactly five minutes? Exam #2 1.) In 2004, the total payroll for the New York Yankees was $182,835,513. They paid Alex Rodriguez $21,726,881. What was Rodriguez' salary as a percentage of the total team payroll? (data from http://www.businessofbaseball.com/) 2.) Juan Pierre of the Florida Marlins was paid $600,000 in 2002. For 2003, his salary went up 66.6667%. For 2004, his salary went up 140%. What was his 2004 salary? (data from http://www.businessofbaseball.com/) 3.) In 2004, Bobby Abreu of the Philadelphia Phillies made a salary of $10,600,000. That was an increase of 16.4835% from his 2003 salary. What was Abreu's 2003 salary? (data from http://www.businessofbaseball.com/) 4.) The price of a sofa was $930. Two weeks ago the price was dropped 15%. This week it was dropped 10%. What is the price now? 5.) In 1988, the New York Mets hit 152 home runs as a team. The following chart shows the distribution of home runs broken down by home runs hit by Lenny Dykstra, Mookie Wilson, Kevin Elster, Gary Carter, Keith Hernandez, Howard Johnson, Kevin McReynolds, Darryl Strawberry and "other" players. Other Strawberry Dykstra Wilson Elster Carter McReynolds Hernandez Johnson a.) The portion of the pie for Darryl Strawberry has an angle of 92.36842. How many home runs did he hit? b.) Three players hit more than 20 home runs. Who were they? c.) How many home runs did Wally Backman hit? d.) Who hit more home runs, Kevin McReynolds or Keith Hernandez? 6.) a.) Write 5.3 x 1011 in regular notation. b.) Write 2.2 x 10-8 in regular notation. c.) Write 32,000,000,000 in scientific notation. d.) Write 0.000000000425 in scientific notation. e.) Use the scientific notation in part a.) and b.). Multiply the two numbers together, SHOWING ALL NECESSARY WORK AND WITHOUT USING YOUR CALCULATOR, and write your final answer in scientific notation. 7.) Estimate the total number of hamburgers eaten each year by left-handed Americans. Be sure to clearly state all of your assumptions. 8.) You put $3500 in the bank. The account gets an annual percentage rate of interest of 2.1% compounded monthly. The money is left in the account for 4 years. Throughout the problem, we assume no other money is added or removed from the accounts. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money you will have at the end of four years. b.) WITHOUT SIMPLIFYING ANYTHING, insert the numbers into the formula you will use to find the amount of money you will have at the end of four years. c.) How much money will you have at the end of four years? 9.) A person is interested in finding out the average income of people in Arkansas. In order to do that, he does a survey by asking the annual income of Arkansas residents who are shopping at Wal-Mart. Are his results likely to be representative of Arkansas? Why or why not? 10.) You start putting money in your retirement fund at age 23. You put in $225 each month. The interest of 10.185% is compounded quarterly. You will retire when you turn 65. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money in your fund when you retire. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the formula. c.) How much money will you have at age 65? d.) What is the total of all of your payments? e.) Find the amount of interest you will receive. 11.) You are buying a house. After the down payment, you need to borrow $105,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 15 year mortgage is 5.275%. Throughout the problem we will ignore escrow payments that might be added to the payment for insurance and taxes. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the monthly payment on this loan. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the formula. c.) What will be your monthly payment? d.) What will be the total of all of your monthly payments? e.) How much interest will you pay over the life of the loan? 12.) You are buying a car. You are going to borrow $24,500 to pay off the car. The interest rate for your 6 year loan is 2.25%. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the monthly payment on this loan. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the formula. c.) What will be your monthly payment? d.) What will be the total of all of your monthly payments? e.) How much interest will you pay over the life of the loan? 13.) The following chart gives historic population data for Russellville, Arkansas.